lemma

What problem does it solve? Mathematical arguments often contain hidden gaps — circular steps, one-directional inequalities, unjustified assumptions — that license false conclusions with the authority of math. This Skill rigorously proves or disproves claims, checks proofs for gaps, and pins down the exact conditions under which results hold. ## Core Features & Use Cases - Proof construction and verification: Works through derivations step by step, with every step justified by a named rule, definition, or cited theorem, and flags any step it cannot close. - Counterexample hunting: Attempts to falsify claims before asserting truth, producing concrete counterexamples when a claim is false along with the corrected statement. - Condition and tightness analysis: States the exact hypotheses a result needs and checks whether bounds are tight or loose, including equality conditions. - Use Case: A user claims their divide-and-conquer algorithm is O(n log n). The Skill walks the recurrence, catches that the merge step was miscounted as O(1) instead of O(n), applies the Master theorem, and confirms the bound with correct reasoning. ## Quick Start Ask the assistant to check whether your derivation or complexity bound is mathematically correct and to show each justified step.